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Articles 271 - 300 of 305

Full-Text Articles in Controls and Control Theory

Using Of Parametric Nonlinear Lc-Circuits In Stabilized Transducers Of The Number Of Phases, Ivan Mikhaylovich Bedritsky, Kamila Komilovna Jurayeva, Laziz Kholboboyevich Bozorov Jun 2020

Using Of Parametric Nonlinear Lc-Circuits In Stabilized Transducers Of The Number Of Phases, Ivan Mikhaylovich Bedritsky, Kamila Komilovna Jurayeva, Laziz Kholboboyevich Bozorov

Chemical Technology, Control and Management

The use of nonlinear circuits of an autoparametric nature with inductive and capacitive elements for obtaining the necessary phase shifts in single-phase-three-phase converters is considered. The amplitude-phase relations between the stresses of windings located on different rods of a three-core core are obtained. The conditions under which it is possible to stabilize the stresses of the artificial phases of the Converter, as well as the phase shifts between them, are shown.


Application Of A Convolutional Neural Networks For Images Recognition, Avazjon Rakhimovich Marakhimov, Lyudmila Petrovna Varlamova Jun 2020

Application Of A Convolutional Neural Networks For Images Recognition, Avazjon Rakhimovich Marakhimov, Lyudmila Petrovna Varlamova

Chemical Technology, Control and Management

In the problems of image recognition, various approaches used when the image is noisy and there is a small sample of observations. The paper discusses nonparametric recognition methods and methods based on deep neural networks. This neural network allows you to collapse images, to perform downsampling as many times as necessary. Moreover, the image recognition speed is quite high, and the data dimension is reduced by using convolutional layers. One of the most important elements of the application of convolutional neural networks is training. The article gives the results of work on the application of convolutional neural networks. The work …


Remote Measurement Of Plant Biomass By Picosecond Laser Radiation, Abdushukur Abdugafurovich Mukhamedov, Abdirashid Saribaevich Rysbaev, Shamsiddin Norchaevich Ernazarov Jun 2020

Remote Measurement Of Plant Biomass By Picosecond Laser Radiation, Abdushukur Abdugafurovich Mukhamedov, Abdirashid Saribaevich Rysbaev, Shamsiddin Norchaevich Ernazarov

Chemical Technology, Control and Management

A description is given of a high-speed optical recording system that uses a solid-state yttrium-aluminum garnet Nd3+ laser that generates a train of picosecond laser pulses. It is shown that by registering and temporarily scanning the secondary fluorescence radiation excited by a sequence of picosecond pulses, it is possible to remotely determine the biomass of plants based on a prematurely created bank of laboratory data.


International Higher Education Cooperation Under Conditions Of Fuzzy Terminology: Intellectual Mobility Vector, Ulugbek Vasikovich Mannanov, Igor Ivanovich Gancherenok Jun 2020

International Higher Education Cooperation Under Conditions Of Fuzzy Terminology: Intellectual Mobility Vector, Ulugbek Vasikovich Mannanov, Igor Ivanovich Gancherenok

Chemical Technology, Control and Management

Terminology analysis of higher education internationalization process concerning joint educational programs is fulfilled. Fuzziness of used terminology is demonstrated. Joint higher education establishments development in the framework of fractal model is suggested as a strategic direction of higher education internationalization, enhancement of its quality and a concept of effective intellectual mobility.


Synergetic Control Of Nonlinear Dynamic Objects, Isomiddin Siddikov, Komil Usmanov, Noilakhon Yakubova Jun 2020

Synergetic Control Of Nonlinear Dynamic Objects, Isomiddin Siddikov, Komil Usmanov, Noilakhon Yakubova

Chemical Technology, Control and Management

Considers the synthesis of effective control algorithms for a chemical reactor, which is the main one in the production of butyl alcohol. The method based on synergetic approach for transferring the apparatus from one capacity to another (specified) maintaining the required quality of the target component is proposed in order to ensure the stabilization of the concentration of target component at the outlet of the reactor under the conditions of uncertain disturbances affecting to an object. A mathematical model of the process based on a stoichiometric matrix taking into account the physicochemical properties of the process is developed. The control …


Research Properties Of Solving Problems Of Parametric Optimization, Dilnoz Tulkunovna Muhamediyeva Jun 2020

Research Properties Of Solving Problems Of Parametric Optimization, Dilnoz Tulkunovna Muhamediyeva

Chemical Technology, Control and Management

A model of parametric optimization with fuzzy initial information is constructed. The conditions and areas of application of the main methods of the theory of fuzzy sets in studies of parametric optimization are determined. A connection is established between the stability of parametric optimization problems and fuzzy optimization problems. An algorithm for solving problems by the method of parametric programming is developed for fuzzy given initial information. The admissible region of the parametric programming problem and the value of its objective function at each point of this region depend on the parameter t. A description of the method for solving …


Development Of A Control Device And Algorithm For Autonomous-Moving Systems, Farhod Qosimov, Ru Jiang, Dong Zhang, Mirkhalil Ismailov Jun 2020

Development Of A Control Device And Algorithm For Autonomous-Moving Systems, Farhod Qosimov, Ru Jiang, Dong Zhang, Mirkhalil Ismailov

Chemical Technology, Control and Management

The article is devoted to improving the control and algorithm for Autonomous moving systems. The function of the controller is to provide communication between the control computer and the actuator. The ATmega2560 microcontroller is selected as the main processor. The electrical diagram of additional devices of the microcontroller is formed. Printed circuit boards consisting of separate blocks are made on the basis of the electrical circuit. To exchange information with external systems and process the received data, a special algorithm for the microcontroller has been created. The microcontroller is programmed based on this algorithm. The analysis of the functioning of …


Extraction Of Chitosan From Died Honey Bee Apis Mellifera, Gulnora Akmalovna Ixtiyarova, Dilshoda Azamovna Hazratova, Bobur Nosir O’G’Li Umarov, Oksana Muratbayevna Seytnazarova Jun 2020

Extraction Of Chitosan From Died Honey Bee Apis Mellifera, Gulnora Akmalovna Ixtiyarova, Dilshoda Azamovna Hazratova, Bobur Nosir O’G’Li Umarov, Oksana Muratbayevna Seytnazarova

Chemical Technology, Control and Management

This article presents the results of obtaining biopolymers of chitin and chitosan from a new promising source- died honey bee apis mellifera. To obtain chitin, at the first stage, the protein (deproteination) and mineral (demineralization) constituents of subpestilence, i.e. put them in soluble state and removed. Demineralization was carried out with 2 M hudrochloric acid for 5 hours at room temperature. The process of deproteination is carried out by processing the crushed raw materials with 1 N sodium hudroxide solution for 1 hour at a temperature of 800С. Each process was accompanied by washing the raw materials to …


Mathematical Modeling Of Thermal Processes Of Traction Asynchronous Engines For Diagnosis And Control Of Their Technical Condition, Nilufar Rabbanaqulovna Avezova, Javharbek Sulton Ugli Fayzullayev Jun 2020

Mathematical Modeling Of Thermal Processes Of Traction Asynchronous Engines For Diagnosis And Control Of Their Technical Condition, Nilufar Rabbanaqulovna Avezova, Javharbek Sulton Ugli Fayzullayev

Chemical Technology, Control and Management

Mathematical models of thermal processes of traction asynchronous motors are developed. A traction asynchronous motor is considered as a thermal system consisting of three bodies (stator winding, stator magnetic core and rotor), which take into account the heat exchange not only between the corresponding bodies, but also the heat exchange between each body and the environment. It is shown that the steady excess of the stator winding temperature of a traction asynchronous motor depends on the multiplicity of the stator winding current, the coefficient of electrical energy loss, and also on the temperature coefficient of the resistance of the winding …


Precise Measuring Cells For Quantitative And Qualitative Measurement, A.A. Begunov, B.M. Akhmedov, R.A. Ibragimov Feb 2020

Precise Measuring Cells For Quantitative And Qualitative Measurement, A.A. Begunov, B.M. Akhmedov, R.A. Ibragimov

Chemical Technology, Control and Management

The main provisions considered in assessing the accuracy of methods and measurement results are considered. It is shown that in the experimental assessment of various accuracy indicators, and also when analyzing the content of components in various gaseous media, the sorption-gravimetric measurement method is widely used, methods for measuring the mass of the sorbent and possible sources of error of this technique. Methods of measuring the mass of gas using specific surface areas, including taking into account the contact of gas with a solid material, and also, the amount of adsorbed gas and its pressure, temperature, type and size of …


Controlling And Forecasting The Reliability Of Integrated Circuits Of Radio Systems Transmitting Information, Abdulaziz M. Nazarov Prof, Dilmurod A. Davronbekov Prof. Feb 2020

Controlling And Forecasting The Reliability Of Integrated Circuits Of Radio Systems Transmitting Information, Abdulaziz M. Nazarov Prof, Dilmurod A. Davronbekov Prof.

Chemical Technology, Control and Management

The issues of forecasting the reliability of integrated circuits, which are the main element base of modern radio engineering information transmission systems, are considered. Methods of parametric and functional control are described to determine the correspondence of the static and dynamic parameters of microcircuits to the required values. A combined method for determining the operating parameters of microcircuits is also described. The advantage of this method in addition to the two above methods is indicated that it combines the function of controlling the operation of the entire control system. Two approaches for predicting reliability are given, as well as mathematical …


Features Of Hydration Process, Structure Formation And Curing Processes Of Mono And Polymineral Cement In The Presence Of Additives Of Solid Waste Of Soda Production, Nargis Shamadinova, Gulnora Abdukadirovna Tokhtakhunova Phd, Temur Azimovich Atakuziev, Shakhnoza Saidanvarovna Rakhimjanova Feb 2020

Features Of Hydration Process, Structure Formation And Curing Processes Of Mono And Polymineral Cement In The Presence Of Additives Of Solid Waste Of Soda Production, Nargis Shamadinova, Gulnora Abdukadirovna Tokhtakhunova Phd, Temur Azimovich Atakuziev, Shakhnoza Saidanvarovna Rakhimjanova

Chemical Technology, Control and Management

The influence of the additive of solid waste of soda production (SWSP) on the content of -C2S and C3S in cement studied. It was found that SWSP affects the density of the aluminum-containing minerals C3A and C4AF, in addition, in the presence of gypsum, their plasticizing properties improved. The introduction of SWSP additives during grinding of clinker intensifies the grinding process and made it possible to obtain a more plastic cement. It was proved that SWSP with CaCl2 content can be used as an additive to concrete and cement mortars - …


Investigating The Solution Properties Of Population Model Of Cross-Diffusion Model With Double Nonlinearity And With Variable Density, Dildora Kabilovna Muhamediyeva Feb 2020

Investigating The Solution Properties Of Population Model Of Cross-Diffusion Model With Double Nonlinearity And With Variable Density, Dildora Kabilovna Muhamediyeva

Chemical Technology, Control and Management

The models of two competing populations with double nonlinear diffusion and three types of functional dependencies are considered. The first dependence corresponds to the Malthusian type, the second to the Verhühlst type (logistic population), and the third to Olli-type populations. A common element of this kind of description is the presence of a linear source. Nonlinear sinks are also present in descriptions of populations of the Verhulst and Ollie type. Suitable initial approximations for a rapidly converging iterative process are proposed. Based on a self-similar analysis and comparison of the solutions of the Cauchy problem in the domain for an …


Techniques To Solve Decision-Making Problems, Dilnoz Tulkunovna Muhamediyeva, Bekmuratov Fayzievich Tulkun Feb 2020

Techniques To Solve Decision-Making Problems, Dilnoz Tulkunovna Muhamediyeva, Bekmuratov Fayzievich Tulkun

Chemical Technology, Control and Management

Solving decision-making problems in poorly formalized systems only with the help of deterministic and probabilistic methods is insufficient. To do this, it is necessary to widely apply the methods of hybrid intelligent systems and, especially, the methods of “soft” calculations (SoftCalculation, SoftComputing) and the directions of ComputationalIntelligence — intelligent computing technologies that are emerging on this theoretical and methodological base. An immune - fuzzy algorithm for the synthesis of fuzzy inference systems (FIS) is proposed. A two-stage adaptive FIS synthesis algorithm is described. At the first stage, the initial fuzzy parameters are clustered in order to reduce the number of …


Neuro-Fuzzy Modeling For Predictive Control Systems With Complex Technological Processes And Production, Yusupbekov Nodirbek, Shukhrat Gulyamov, Malika Doshchanova Feb 2020

Neuro-Fuzzy Modeling For Predictive Control Systems With Complex Technological Processes And Production, Yusupbekov Nodirbek, Shukhrat Gulyamov, Malika Doshchanova

Chemical Technology, Control and Management

The paper implements a modification of a fuzzy neural network, which is suitable for predictive control purposes. Adaptation of a multidimensional programmable controller based on a neural algorithm for the back propagation of forecasting errors is proposed, as well as neural parametric identification of a fuzzy mathematical model of complex technological processes and production based on experimental data and expert estimates.


Steady Algorithms For Synthesis Of Multidimensional Controlling Systems With Incomplete Information About The Object State, Uktam Farkhodovich Mamirov Feb 2020

Steady Algorithms For Synthesis Of Multidimensional Controlling Systems With Incomplete Information About The Object State, Uktam Farkhodovich Mamirov

Chemical Technology, Control and Management

In this paper, questions of forming and creation of steady synthesis algorithms of multidimensional controlling systems at incomplete information on object status are considered. It is shown that the matrix of feedback coupling on a status at the complete information is not determined. The different algorithms of steady calculation of a matrix pseudo-inverse to the matrix of outputs using these or those decomposition of matrixes are analyzed. Algorithms of iterative specification of a required solution of "skeletal" decomposition are given. The given expressions allow synthesizing the simplified computing procedures of synthesis of multidimensional controlling systems at incomplete information on object …


Importance Of Morphological Features In Orthoptera Identification, Kamilov Mirzoyan, Alisher Khamroev, Hudayberdiev Mirzaakbar Feb 2020

Importance Of Morphological Features In Orthoptera Identification, Kamilov Mirzoyan, Alisher Khamroev, Hudayberdiev Mirzaakbar

Chemical Technology, Control and Management

This article analyzes the problems of implementing image recognition methods and algorithms for identifying biological objects. The Orthoptera group was chosen as a biological object. Orthoptera is a taxonomic order of insects that includes grasshoppers, crickets, locusts, and others. Approaches to the formation and identification of features of Orthoptera species and the formation of training and control samples of their samples are proposed. Estimation algorithms (ACE) were chosen as algorithmic support for identifying Orthoptera collections. ACE is based on the principle of partial priority. Approaches to the formation of a training and testing complex based on the data from the …


The Potentials Of Faecal Sludge Treatment Using Local Conditioners In Tanzania: A Review, Doglas Benjamin1 Dec 2019

The Potentials Of Faecal Sludge Treatment Using Local Conditioners In Tanzania: A Review, Doglas Benjamin1

Tanzania Journal of Engineering and Technology (TJET)

Worldwide, every day human beings generate millions of tons of Faecal Sludge (FS), which is rich in water, nutrients, energy, and organic compounds. Yet FS is not being managed in a way that permits us to derive value from its reuse, while at the same time, millions of farmers struggle with depleted soils and lack of water. In most of the developing countries, energy for cooking is mainly derived from cutting of trees, either as wood or charcoal. Resource recovery and reuse from FS can create livelihoods, enhance food security, support green economies, reduce waste and contribute to cost recovery …


Process/Equipment Design Implications For Control System Cybersecurity, Helen Durand Jul 2019

Process/Equipment Design Implications For Control System Cybersecurity, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

An emerging challenge for process safety is process control system cybersecurity. An attacker could gain control of the process actuators through the control system or communication policies within control loops and potentially drive the process state to unsafe conditions. Cybersecurity has traditionally been handled as an information technology (IT) problem in the process industries. In the literature for cybersecurity specifically of control systems, there has been work aimed at developing control designs that seek to fight cyberattacks by either giving the system appropriate response mechanisms once attacks are detected or seeking to make the attacks difficult to perform. In this …


Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu May 2019

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the …


On Accounting For Equipment-Control Interactions In Economic Model Predictive Control Via Process State Constraints, Helen Durand Feb 2019

On Accounting For Equipment-Control Interactions In Economic Model Predictive Control Via Process State Constraints, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Traditionally, chemical processes have been operated at steady-state; however, recent work on economic model predictive control (EMPC) has indicated that some processes may be operated in a more economically-optimal fashion under a time-varying operating policy. It is unclear how time-varying operating policies may impact process equipment, which must be investigated for safety and profit reasons. It has traditionally been considered that constraints on process states can be added to EMPC design to prevent the controller from computing control actions which create problematic operating conditions for process equipment. However, no rigorous investigation has yet been performed to analyze whether, when a …


Operation And Process Control Development For A Pilot-Scale Leaching And Solvent Extraction Circuit Recovering Rare Earth Elements From Coal-Based Sources, Douglas Kweku Addo Jan 2019

Operation And Process Control Development For A Pilot-Scale Leaching And Solvent Extraction Circuit Recovering Rare Earth Elements From Coal-Based Sources, Douglas Kweku Addo

Theses and Dissertations--Mining Engineering

The US Department of Energy in 2010 has identified several rare earth elements as critical materials to enable clean technologies. As part of ongoing research in REEs (rare earth elements) recovery from coal sources, the University of Kentucky has designed, developed and is demonstrating a ¼ ton/hour pilot-scale processing plant to produce high-grade REEs from coal sources. Due to the need to control critical variables (e.g. pH, tank level, etc.), process control is required. To ensure adequate process control, a study was conducted on leaching and solvent extraction control to evaluate the potential of achieving low-cost REE recovery in addition …


A Nonlinear Systems Framework For Cyberattack Prevention For Chemical Process Control Systems, Helen Durand Sep 2018

A Nonlinear Systems Framework For Cyberattack Prevention For Chemical Process Control Systems, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Recent cyberattacks against industrial control systems highlight the criticality of preventing future attacks from disrupting plants economically or, more critically, from impacting plant safety. This work develops a nonlinear systems framework for understanding cyberattack-resilience of process and control designs and indicates through an analysis of three control designs how control laws can be inspected for this property. A chemical process example illustrates that control approaches intended for cyberattack prevention which seem intuitive are not cyberattack-resilient unless they meet the requirements of a nonlinear systems description of this property.


Economic Model Predictive Control Design Via Nonlinear Model Identification, Laura Giuliani, Helen Durand Aug 2018

Economic Model Predictive Control Design Via Nonlinear Model Identification, Laura Giuliani, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Increasing pushes toward next-generation/smart manufacturing motivate the development of economic model predictive control (EMPC) designs which can be practically deployed. For EMPC, the constraints, objective function, and accuracy of the state predictions would benefit from process models that describe the process physics. However, obtaining first- principles models of chemical process systems can be time-consuming or challenging such that it is preferable to develop physics-based process models automatically from process operating data. In this work, we take initial steps in this direction by suggesting that because experiments that are used to characterize first-principles models often target specific types of data, an …


State Measurement Spoofing Prevention Through Model Predictive Control Design, Helen Durand Aug 2018

State Measurement Spoofing Prevention Through Model Predictive Control Design, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Security of chemical process control systems against cyberattacks is critical due to the potential for injuries and loss of life when chemical process systems fail. A potential means by which process control systems may be attacked is through the manipulation of the measurements received by the controller. One approach for addressing this is to design controllers that make manipulating the measurements received by the controller in any meaningful fashion very difficult, making the controllers a less attractive target for a cyberattack of this type. In this work, we develop a model predictive control (MPC) implementation strategy that incorporates Lyapunov-based stability …


Data-Based Nonlinear Model Identification In Economic Model Predictive Control, Laura Giuliani, Helen Durand Jul 2018

Data-Based Nonlinear Model Identification In Economic Model Predictive Control, Laura Giuliani, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Many chemical/petrochemical processes in industry are not completely modeled from a first-principles perspective because of the complexity of the underlying physico-chemical phenomena and the cost of obtaining more accurate, physically relevant models. System identification methods have been utilized successfully for developing empirical, though not necessarily physical, models for advanced model-based control designs such as model predictive control (MPC) for decades. However, a fairly recent development in MPC is economic model predictive control (EMPC), which is an MPC formulated with an economics-based objective function that may operate a process in a dynamic (i.e., off steady-state) fashion, in which case the details …


Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu Feb 2018

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right halfplane, and the other moves to the left half-plane. When the parameters move into the …


Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar Jan 2018

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …


Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar Jan 2018

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . , K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delay-per-scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between …


Process Control Laboratory Skid Refurbishment, Danny Crowder Jan 2017

Process Control Laboratory Skid Refurbishment, Danny Crowder

Williams Honors College, Honors Research Projects

This project evaluates a salvaged process control skid for potential refurbishment and educational re-use. In-lab work evaluated the existing skid. Several process control elements have been recommended for replacement, including the process tank (due to corrosion), the pressure transmitter (operability/corrosion), the flow meters (mechanical) and the control system (age). The control valves, temperature elements and transmitters, pump, holding tanks, and the electrical heat exchanger should be salvaged. An I/P converter and pressure relief valve should be added to the pneumatic feed. Enclosing of all electrical components should be prioritized. An electrical schematic for a new control system should be implemented. …